- #1
dykuma
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Homework Statement
A mass M falls under gravity (force mg) through a liquid with decreasing viscosity so that the retarding force is -2mv/(1+t). If it starts from rest, what is the speed, acceleration, and distance fallen at time t=1.
Homework Equations
F=ma
The Attempt at a Solution
F = 2mv/(1+t) - mg
F = m[- g + 2v/(1+t)]
ma = m[-g + 2v/(1+t)]
a = -g + 2v/(1+ t)
At this point, I see two paths to a solution, and I don't know which is correct.
I can let a=x'', v=x'
x'' - (2/(1+ t)) x' = -g
where the solution according to mathmatica is (I'm not sure how to solve this exactly, my guess is to use frobenius)
x =1/3 - C1 T^3 + 1/2(2 C1 + g) T^2 + g T + C1 T + C2
or I can let
a=v'
v' = -g + 2v/(1+ t)
v' - 2v/(1+ t)= -g
Where the solution would be
v = (1 + t) (C1 t + C1 + g) - Edit (I see this solution might be wrong, checking now)
I'm not sure which is the correct result, and I am concerned about the units on each,
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